I can say with 95% certainty that those are seismic cable restrainers. Our office has designed about a dozen of these for various bridges around my state.
The thing that gives me pause is that the bridge does not look that old, and yet these are typically installed on older bridges. They are used because the older bridges never considered the ramifications of seismic displacement. Based on your seismic analysis, if any of the following are true, the bridge could be a good candidate for cable restrainers:
1. Bridge bearings are not sufficient to resist the expected levels of displacement and bearing failure is a possibility.
2. Girder seat length is not long enough and your girder could potentially fall off the seat
3. At expansion piers, out of phase superstructure movement is excessive enough to cause large openings at deck joints and you want to limit their relative movement away from each other.
I am not 100% certain what the bulbous caps on the end are, but my guess is that they are either grease caps or anti-tampering caps. The ones that we have designed use a bearing nut and a jamb nut. The bearing nut is not fit snug to the face of the beam since we need to allow for a small amount of serviceable movement for every-day use. For seismic events, where the movement is higher, the nut will engage.
Further observations, from where I come from, that is one strange bridge design..... Lateral bracing at the top and bottom and only at the end bay!? Mid-height, short diaphragms with varying flange width..... (3) Intermediate added flanges along the web!?